Question

determine the largest open intervals of the domain over which the function is continuous. select the correct choice below and, if necessary, fill in the answer box within your choice. a. the function is not continuous over all real numbers, and the largest open interval(s) of the domain over which the function is continuous is/are . (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is continuous everywhere. c. the function is not continuous anywhere.

Explanation:

Step1: Recall continuity concept

A function is continuous on an open - interval if there are no breaks, jumps, or holes in the graph of the function on that interval.

Step2: Analyze the graph

Looking at the given graph, we can see that the function has a break at \(x = 0\). The function is continuous on the intervals \((-\infty,0)\) and \((0,\infty)\).

Answer:

A. The function is not continuous over all real numbers, and the largest open intervals of the domain over which the function is continuous are \((-\infty,0),(0,\infty)\)